Step 1

Whisk mayonnaise, lemon juice, horseradish, and 1/4 teaspoon salt in a medium bowl; add pepper to taste. Refrigerate until ready to serve.

Step 2

Crack egg into a medium bowl and add egg white; whisk until lightly beaten. Add salmon, mustard, remaining 1/2 teaspoon salt, and pepper to taste. Stir with a fork until mostly smooth (it's OK if small salmon chunks remain). Stir in parsley and bread crumbs. Shape mixture into 4 (about 1/2-inch-thick) patties.

Step 3

Heat oil in a large nonstick skillet over medium. Add patties; cook, flipping once, until firm and golden, about 3 minutes per side.

Step 4

Spread mayonnaise mixture evenly on cut sides of buns. Top bottom buns with watercress and salmon patties. Replace top buns and serve.